Problem: Solve for $x$ and $y$ using elimination. ${6x+5y = 57}$ ${-5x+4y = 26}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $5$ ${-24x-20y = -228}$ $-25x+20y = 130$ Add the top and bottom equations together. $-49x = -98$ $\dfrac{-49x}{{-49}} = \dfrac{-98}{{-49}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {6x+5y = 57}\thinspace$ to find $y$ ${6}{(2)}{ + 5y = 57}$ $12+5y = 57$ $12{-12} + 5y = 57{-12}$ $5y = 45$ $\dfrac{5y}{{5}} = \dfrac{45}{{5}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {-5x+4y = 26}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + 4y = 26}$ ${y = 9}$